Question

if sec theta = 5/4,then tan theta /2

Answer 1

Sec θ = 5/4

By using the formula,
tan²θ = sec²θ -1
         = (5/4)²-1
         = 25/16 - 1
         = 9/25

⇒ tanθ  = 3/5

tanθ/ 2 = (3/5)/2
            =3/10

∴ tanθ/ 2 = 3/10

Answer 2

Answer:

$\tan(\frac{\theta}{2})=\pm\frac{1}{3}$

Step-by-step explanation:

Given : $\sec\theta=\frac{5}{4}$

To find : The value of $\tan (\frac{\theta}{2})$

Solution :

$\sec\theta=\frac{5}{4}$

So, $\cos\theta=\frac{1}{\sec\theta}=\frac{4}{5}$

We know,

$\tan(\frac{\theta}{2})=\pm\sqrt{\frac{1-\cos\theta}{1+\cos\theta}}$

$\tan(\frac{\theta}{2})=\pm\sqrt{\frac{1-\frac{4}{5}}{1+\frac{4}{5}}}$

$\tan(\frac{\theta}{2})=\pm\sqrt{\frac{\frac{5-4}{5}}{\frac{5+4}{5}}}$

$\tan(\frac{\theta}{2})=\pm\sqrt{\frac{\frac{1}{5}}{\frac{9}{5}}}$

$\tan(\frac{\theta}{2})=\pm\sqrt{\frac{1}{9}}$

$\tan(\frac{\theta}{2})=\pm\frac{1}{3}$

Therefore, The value is $\tan(\frac{\theta}{2})=\pm\frac{1}{3}$